direct product and direct sum of groups

[Mattia Villani]

How can I calculate the direct product of two groups and/or the direct sum?

For example given:

G.<x,y>=FreeGroup()

H=G.quotient([x*y])

how do I calculate H+H and HxH?

[slelievre]

2021-03-24 14:53:06 UTC, Matt:

Having defined `H`, you can type

    H.

then hit the TAB key to see what methods are available.

This reveals the methods `cartesian_product`

and `direct_product`, are they what you need?

```

sage: G.<x, y> = FreeGroup()

sage: H = G.quotient([x*y])

sage: H.cartesian_product(H)

The Cartesian product of

(Finitely presented group < x, y | x*y >,

 Finitely presented group < x, y | x*y >)

sage: H.direct_product(H)

Finitely presented group < a, b, c, d |

    a*b, c*d, a^-1*c^-1*a*c, a^-1*d^-1*a*d,

    b^-1*c^-1*b*c, b^-1*d^-1*b*d >

```

[Dima Pasechnik]

careful here, FreeGroup is not Abelian, you'll want to add commuting relations
for all its generators.

You might prefer AbelianGroup() to begin with.


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